| > what are the concrete benefits relative to traditional vectors, matrices, quaternions? Traditional vectors are fine, but things get ugly when you do things like cross products. People should really just use bivectors. It is conceptually simpler and doesn't entail arbitrary sign conventions. Matrices are way too general a tool to criticize them as a whole. Using them makes sense for some problems, and much less sense for others. As far as I understand it though, GA is not really competing with matrices as a tool to do linear algebra. GA is mainly about geometry, and not all linear algebra is about geometry. Quaternions really are bivectors behind the scene. Exposing them as such would make them much easier to understand. And I don't think we would necessarily lose in performance. It could just be a matter of notation really. Instead of naming them i, j and k, we should name them jk, ki and ij respectively. At the cost of a sign change, we would make them simpler to understand imho. > how would you characterize the power / utility of (U)GA? I'm afraid I'm not qualified to make the case for GA. People much smarter than me did, and since you're interested you probably know them (David Hestenes, Chris Doran...). Me, I'm convinced and charmed, but I'm just a hobbyist who would like to do 3D graphics elegantly. |